The Catechism in Questions & Answers

604. How did the Catholic Apostolic Church come into being?

In 1835, the Apostles withdrew to Albury for a year of intensive deliberations together. They developed the “Great Testimony” (1837), a confessional text that was made available to all spiritual and secular leaders of Christendom.
In this document the Apostles called upon Christians to gather under their leadership and thereby prepare themselves for the return of Christ. They were thus not interested in establishing a new church, but rather in bringing the various existing churches together under the leadership of Apostles.
The majority of Christians did not accept the call of the Apostles, however. The few Christians that did believe the Apostles banded together in a new church, namely the Catholic Apostolic Church.